Let f be a polynomial function of degree 3 satisfying f(1)=3, f(2)=5 and f(3)=7 . If product of the roots of the equation (f(x))^2+4 x f(x)+3 x^2=0 is 4 and the sum of all possible values of f(4) is k then find [k] . [Note: [y] denotes grea

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Let f be a polynomial function of degree 3 satisfying f(1)=3, f(2)=5 and f(3)=7 . If product of the roots of the equation (f(x))^2+4 x f(x)+3 x^2=0 is 4 and the sum of all possible values of f(4) is k then find [k] . [Note: [y] denotes greatest integer function less than or equal to y .]

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Correct answer: 20

aligned f(x) & =a(x-1)(x-2)(x-3)+2 x+1 (f(x))^2+4 x f(x)+3 x^2 & =0 aligned Product of the roots, (1-6 a)^2 a^2 =4 1-6 a= 2 a array l a=1 / 8 a=1 / 4 array . aligned & & f(4)=6 a+9 < _ a=1 / 4 ^ n=1 / 8 - 3 4 +9 & k=20+ 1 4 [k]=20 & aligned

Let f be a polynomial function of degree 3 satisfying f(1)=3, f(2)=5 and f(3)=7 . If product of the roots of the equation (f(x))^2+4 x f(x)+3 x^2=0 is 4 and the sum of all possible values of f(4) is k then find [k] . [Note: [y] denotes greatest integer function less than or equal to y .]

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